Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{4}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}15&88\\37&13\end{bmatrix}$, $\begin{bmatrix}35&72\\83&17\end{bmatrix}$, $\begin{bmatrix}89&0\\69&43\end{bmatrix}$, $\begin{bmatrix}109&80\\85&91\end{bmatrix}$, $\begin{bmatrix}109&104\\107&11\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.iy.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $24$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.48.0-8.q.1.3 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
40.48.0-8.q.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.48.0-120.bl.1.11 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.0-120.bl.1.13 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.48.1-120.n.1.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.48.1-120.n.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.192.1-120.qq.1.8 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qq.1.9 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qq.2.6 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qq.2.11 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qr.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qr.1.13 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qr.2.3 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.qr.2.14 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.288.9-120.cjf.1.21 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.384.9-120.wt.1.14 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.480.17-120.np.1.12 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
240.192.3-240.ql.1.8 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ql.1.23 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qp.1.16 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qp.1.21 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qt.1.6 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qt.1.24 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qx.1.14 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.qx.1.22 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sb.1.5 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sb.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sd.1.3 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sd.1.25 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.so.1.7 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.so.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sp.1.7 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.sp.1.29 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ss.1.12 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ss.1.20 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ta.1.4 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.ta.1.24 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.te.1.16 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.te.1.18 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.th.1.8 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.192.3-240.th.1.22 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |